Question

solve this system of equation by using the elimination method and find all four unknown variables. please show the work too. :)
w+x-y+z=0
w-2x-2y-z=-5
w-3x-y+z=4
2w-x-y+3z=7

Answer 1

get three equations by( 2)-(1),(3)-(1),(4)-2(1),we get three equations in x,y,z

Answer 2

similarly then out of three equations make two equations

Answer 3

i dont really understand what you mean surjithayer. can you please show me the steps on how to ow to do it plz. :)

Answer 4

This can be solved using the "elimination method" many ways using different steps. You will need to understand the concept. You will try to eliminate the variable by using algebra and combining equations so the variable you want to eliminate is cancelled out by either subtracting or adding two equations, you will continue to do this until you are able to solve for one variable, which value you will then substitute in the original equations and continue on until all the variables have been solved. One person will travel a different path than another, but in the end the solution will evolve. I will show you the steps that I took, if you are willing to work with me.

Answer 5

Equation No. 1 w+x-y+z=0
Equation No. 2 w-2x-2y-z=-5
Equation No. 3 w-3x-y+z=4
Equation No. 4 2w-x-y+3z=7
I have repeated the 4 equations and labeled them 1 thru 4. Whenever I get an answer from you we will start.

Answer 6

I am ready to work with you and i am sorry that i didnt reply sooner.

Answer 7

O.K, that is the right attitude. I want to solve for x first, because I see a way to eliminate w, y, and z. @kimberly123 Please observe equation No. 1 and No. 3 and note that in both of them, w, y, and z have the same coefficient, namely a 1 and each variable coefficient is the same sign, that makes this a good choice to eliminate them and solve for x.

w + x - y + z = 0
w -3x -y + z = 4 note that the coefficient of the w y and z are equal in value & sign.

Answer 8

oh ok i understand so we are going to use equation 1 and 3 first since they have the same signs.

Answer 9

I will multiply equation No. 3 by a -1 getting:

-w + 3x + y - z = -4 this is legal as I multiplied BOTH sides of the equal sign. Now I add
w + x -y +z = 0 Equation No. 1
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4x = -4 and solve for x
4x = -4
x=-4/4 = -1

Do you see how we got x?

Answer 10

ohh! yes i understand it. so to summarize you multiplied -1 with equation 3 in order to change the signs of the third equation so that you could eliminate them and thats when you did a normal 2 step equation. so then how do you get the answer for the rest of the variables?

Answer 11

Excellent, exactly, I couldn't of said it any better. Now will take the original equations and substitute (-1) for all the x variables. Like so:
w+(-1)-y+z=0
w-2(-1)-2y-z=-5
w-3(-1)-y+z=4
2w-(-1)-y+3z=7 Simplifying they become:

w - y + z =1
w - 2y - z = -7
w -y + z = 1
2w - y + 3z = 6 Note that 1 and 3 are alike so we now only need to look at 1, 2, and 4 to plan on getting rid of a variable w, y, or z. Did you follow that simplification process, we just substituted the value -1 that we found for x into the x.

Answer 12

yes sir i got how you did it! :)

Answer 13

so what do you do next?

Answer 14

Lets eliminate w and z and solve for y.
I take the w - y + z =1 and add the
w-2y - z=-7
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2w-3y = -6 Remember this (z is now gone)
Now take the w-2y -z equation and multiply it by 3 getting 3w -6y - 3z = -21 and add our 4th equation (simplified) getting:
3w - 6y -3z =-21
2w - y +3z =6
-----------------
5w - 7y =-15 Note z is gone here Now to solve for y remember that equation I told you to remember, get it and lets add some more getting this:
2w - 3y = -6
-5w + 3y = 15
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-3w=9
w=-3 Substitute this in 2w - 3y = -6 and solve for y
-6 - 3y =-6
-3y = 0
y=0

we now havde x=-1, w=-3, y=0 we can substitute these in the Original No. 1 and solve for z which is 4

Answer 15

wow i get it now thank you so much for your help i wish you can be my teacher! :D

Answer 16

do you think you can help me with a question about area? i am having trouble solving it .

Answer 17

Good luck, the important thing is the concept, this problem was long, and subject to some mistakes, so it is always a good and substitute your solution in all of the original equations. since one value was a 0, mistakes are likely to be made.

Answer 18

Well if it is a short one I have to leave here in 30 min.

Answer 19

ohh do you think i can ask you the question another time?

Answer 20

If I am on line, what is the area question?

Answer 21

It says find the area of the shaded region and then there is a picture.